## Residues and the Zeta function

Show that the residue of $\frac{\zeta^4(s)}{\zeta(2s)}\frac{x^{s+1}}{s(s+1)}$ at $s=1$ takes the form $x^2P(\log{x})$, where $P$ is a cubic polynomial. (Here, $\zeta(s)$ refers to the Riemann zeta-function.)